A special purpose linear programming algorithm for obtaining least absolute value estimators in a linear model with dummy variables

References

• Armstrong , R. D. and Frome , E. L. 1976 . A comparison of two algorithms for absolute deviation curve fitting . J. Amer. Statist. Assoc. , 71 : 328 – 330 .
   Web of Science ®Google Scholar
• Armstrong , R. D. and Hultz , J. W. 1977 . A restricted discrete approximation problem in the L1 norm . SIAM J. Numer. Analysis , 14 : 555 – 565 .
   Web of Science ®Google Scholar
• Barrodale , I. 1968 . L1 approximation and the analysis of data . Appl. Statist. , 17 : 51 – 57 .
   Web of Science ®Google Scholar
• Barrodale , I. and Roberts , F. D. K. 1973 . An improved algorithm for discrete L1 linear approximation . SIAM J. Numer. Analysis , 10 : 839 – 848 .
   Web of Science ®Google Scholar
• Barrodale , I. and Roberts , F. D. K. 1974 . Solution of an over-determined system of equations in the L1 norm . Commun. Assoc. Comput. Mach. , 17 : 319 – 320 .
   Web of Science ®Google Scholar
• Bartels , R. H. and Golub , G. H. 1969 . The simplex method of linear programming using LU decomposition . Commun. Assoc. Comput. Mach. , 12 : 266 – 268 .
   Web of Science ®Google Scholar
• Charnes , A. 1952 . Optimality and degeneracy in linear programming . Econometrica , 20 : 160 – 170 .
   Web of Science ®Google Scholar
• Charnes , A. and Cooper , W. W. 1961 . Management Models and Industrial Applications of Linear Programming Vol. I, II ,
   Google Scholar
• Charries , A. , Cooper , W. W. and Ferguson , R. 1955 . Optimal estimation of execution compensation by linear programming . Management Sci. , 2 : 138 – 151 .
   Google Scholar
• Cline , A. K. 1976 . A descent method for the uniform solution to overdetermined systems of linear equations . SIAM J. Numer. Analysis , 13 : 293 – 309 .
   Web of Science ®Google Scholar
• Dantzig , G. B. and Van , Slyke R. M. 1967 . Generalized upper bounding techniques . J. Computer Systems Sci. , 1 : 213 – 226 .
   Google Scholar
• Frome , E. L. and Armstrong , R. D. 1977 . Proc. 10th Ann. Symp. Comput. Sci. Statist Interface . A robust procedure for estimating the trend-cycle component of an economic time series . 1977 . (in press)
   Google Scholar
• Glahe , F. R. and Hunt , J. G. 1970 . The small sample properties of simultaneous equation least absolute estimators vis-avis least squares estimators . Econometrica , 38 742 – 753 .
   Web of Science ®Google Scholar
• Graybill , F. A. 1961 . An Introduction to Linear Statistical Models , New York : McGraw-Hill .
   Google Scholar
• Kiountouzis , E. A. 1973 . Linear programming techniques in regression analysis . Appl. Statist , 22 : 69 – 73 .
   Google Scholar
• Mc Neil , D. R. and Tukey , J. W. 1975 . Higher order diagnosis of two-way tables, illustrated on two sets of demographic empirical distributions . Biometrics , 31 : 487 – 510 .
   PubMed Web of Science ®Google Scholar
• Searle , S. R. 1971 . Linear Models , New York : John Wiley and Sons, Inc .
   Google Scholar
• Snedecor , G. W. and Cochran , W. G. 1967 . Statistical Methods , Ames, IA : Iowa State University Press .
   Google Scholar
• Spyropoulos , K. , Kiountouzis , E. and Young , A. 1973 . Discrete approximations in the L1 norm . The Computer J. , 16 : 180 – 186 .
   Web of Science ®Google Scholar
• Wagner , H. M. 1959 . Linear programming techniques for regression analysis . J. Amer. Statist. Assoc. , 54 : 206 – 212 .
   Web of Science ®Google Scholar